Third-order square-root topological insulators on decorated diamond sonic crystals

• Published in: Journal of physics. Condensed matter 2023-10, Vol.35 (40), p.405001
• Main Authors: Geng, Zhi-Guo, Shen, Ya-Xi, Duan, Liwei, Chen, Zhaojiang, Zhu, Xue-Feng
• Format: Article
• Language: English
• Subjects: sonic crystals; square-root topological insulators; third-order corner states
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/1361-648X/ace1c2

The square-root operation can generate novel topological phases, whose nontrivial topological properties are inherited from the parent Hamiltonian. Here we report the acoustic realization of third-order square-root topological insulators by adding additional resonators between the site resonators of original diamond lattice. Due to the square-root operation, multiple acoustic localized modes appear in doubled bulk gaps. The bulk polarizations of the tight-binding models are employed to reveal the topological feature of the higher-order topological states. By tuning the coupling strength, we find the emergence of third-order topological corner states in doubled bulk gaps on tetrahedron-like and rhombohedron-like sonic crystals, respectively. The shape dependence of square-root corner states provides an extra degree of freedom for flexible manipulation on the sound localization. Furthermore, the robustness of the corner states in three-dimensional (3D) square-root topological insulator is well elucidated by introducing random disorders into the irrelevant bulk region of the proposed 3D lattices. This work extends square-root higher-order topological states into 3D system, and may find possible applications in selective acoustic sensors.